Concept explainers
The rational number
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Calculus (MindTap Course List)
- Prove that 23 is not a rational number.arrow_forwardUse the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that a2=3b2. Explain how this proves that 3 is not a rational number.arrow_forward13. Prove that if and are rational numbers such that then there exists a rational number such that . (This means that between any two distinct rational numbers there is another rational number.)arrow_forward
- Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?arrow_forward23. Find k such that x2+(k+1)x+k+4=0 will have two equal roots.arrow_forward
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